Question

The Navarro Frenk & White (NFW) model describes the (spherically symmetric) haloes of dark matter that form in cosmological simulations. It says that the density of dark matter follows the distribution
+- p(r) = p(-) *-8
, where is the distance from the center of the halo, and is an arbitrary length. Show (using Poisson’s formula) that the potential consistent with this density distribution is $\Phi(r)=-\sigma^2(\frac{r}{a})^{-1}ln(1+\frac{r}{a})$ , where $\sigma^2=4\pi G\rho_{0}a^2$ .

Answer 1

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